MATH+ is delighted to welcome Guido F. Montúfar from the University of California, Los Angeles (UCLA), to the MATH+ community as a Visiting Scholar, hosted by Benjamin Gess at Technische Universität Berlin. The MATH+ Visiting Scholar Program aims to enhance the international profile of MATH+ by providing support for more extended visits by outstanding scientists and scholars from around the world.

This summer, Guido F. Montúfar returns to TU Berlin, bringing his expertise in mathematics, statistics, and machine learning to the institution where his academic career began. He studied mathematics and physics at TU Berlin, earning Diploma degrees in Mathematics (2007) and Physics (2009), before completing his PhD (Dr. rer. nat.) in Mathematics at Universität Leipzig and the Max Planck Institute for Mathematics in the Sciences (MPI MiS) in 2012. Since 2018, Montúfar has led the Mathematical Machine Learning Group at the MPI MiS in Leipzig. He joined the UCLA faculty in 2017, where he is now Professor of Mathematics and Statistics & Data Science.

Montúfar’s research develops the mathematical foundations of modern machine learning, combining ideas from optimization, geometry, algebra, probability, and dynamical systems to understand the principles underlying deep learning. His work has advanced the theory of neural network expressivity, optimization dynamics, implicit bias, feature learning, and the geometry of learning algorithms, with the broader goal of establishing rigorous mathematical foundations for artificial intelligence.

During his visit to TU Berlin from June to July 2026, Montúfar will collaborate closely with Benjamin Gess’s research group and other members of TU Berlin and MATH+. He aims to strengthen interactions within the mathematics and machine learning community in Berlin and develop new research collaborations and projects at the interface of mathematics and artificial intelligence.

Commenting on his research stay in Berlin, he said: “I am delighted to join the MATH+ community as a Visiting Scholar. Berlin has an outstanding mathematical and machine learning research environment, and I am very much looking forward to collaborating with colleagues across the city, discussing new ideas, and contributing through both research and teaching. I hope the visit will lead to lasting collaborations and new mathematical perspectives on modern artificial intelligence.”

Alongside his research activities in Berlin, he will also be engaged in teaching a graduate course titled “Mathematical Foundations of Modern Machine Learning: Parameter Spaces, Function Spaces, and Optimization Dynamics” from 20-24 July.  The course presents a mathematical perspective on modern machine learning centered around three fundamental objects: the parameter spaces of neural networks, the function spaces they realize, and the optimization dynamics that connect the two. Combining mathematical foundations with current research developments, it is intended for graduate students, postdoctoral researchers, and anyone interested in the mathematical theory of machine learning.

LINKS:

• Guido F. Montúfar personal home page
• Benjamin Gess’ personal home page
• MATH+Visiting Scholars program